Yes, it does have to be off of the hook.
The reason you have to lift your hand held receiver on and off the hook, when you are using the headset, is because the headset only replaces the hand held receiver of the telephone. It does not change how the phone functions.
If you do not take the hand receiver off the hook when placing or answering a call, then the call will not come through. If you do not hang it back up when done with the call, the phone will be left off hook, and will appear busy.
In order to Not have to lift your hand held receiver on and off the hook when you use a headset, is if the telephone has what is called an "On-Hook Dialing" feature.
To have this feature, your telephone would either have a dedicated headset jack, so that you may bypass the hand held receiver jack. Or the telephone would have some type of headset programming feature, where you program the telephone for Headset use, then press a designated button on the telephone to answer and hang up calls, when using the headset.
You can look in your telephone's manual or contact the telephone's manufacturer to see if that phone has either of these features.